The first principles here refer to the basic equations of the Standard Model. There were a lot of alternative theories in sixties and seventies but eventually they were disproven experimentally and only SM survived.

But the problem with SM is that when one deals with strong interactions, nobody so far came with good ways to calculate things. For example, in theory the mass of proton can be derived. But in practice it is not. So one uses that as an extra parameter and tries to use that to constrain calculations in other areas.

The data comes in two ways:

1. Hey these particles are interacting with each other (e.g. they attract each other, they repel each other, they combine or split apart into each other, etc...)

2. I have measured something about this interaction (e.g. how fast, how far, how likely, etc...) to within a certain degree of accuracy

Put them together and we have a sparse noisy list of forces, and a list of constants.

Then we come up with theories to explain and reduce the data to their simplest components.

Those theories occasionally spit out that there should be an interaction we haven't seen between some particles yet or a more accurate picture of an interaction we have already seen and we can run some experiments to see if the theory holds true in practice.

We can then check how well those theories work by their predictions.

- Gravity is just varying amounts of positive attraction over unlimited range (i.e. just a positive integer).

- Electromagnetism is varying amounts of positive or negative attraction over unlimited range. (i.e. just an integer)

The problem with strong interactions is that they get messy really fast. The energies and interactions involved are crazy.

- We have the quarks (which are the fundamental matter particles that the strong force interacts on)

- We have the gluons (which are part of the strong force itself)

- And the strong interactions: which are actually 3 different amounts of positive or negative attractions that must all balance out (i.e. a whole bunch of numbers), but they get stronger as they get further away to the point that new particles can be created to reduce the range between any two particles, oh and the gluons can also interact with each other complicating matters further.